НЕЛОКАЛЬНАЯ ЗАДАЧА С ИНТЕГРАЛЬНЫМ УСЛОВИЕМ СКЛЕЙКИ ДЛЯ НАГРУЖЕННОГО УРАВНЕНИЯ СМЕШАННОГО ТИПА С ДРОБНОЙ ПРОИЗВОДНОЙ КАПУТО
Keywords:
Нагруженное уравнение, уравнение параболо-гиперболического типа, оператор дробного порядка в смысле Капуто, интегральное условие склеивания, единственность и существование решенияAbstract
Данная работа посвящена доказательству единственности и существования решения нелокальной задачи с интегральным условием склеивания для нагруженного уравнения параболо-гиперболического типа, включающего оператор Капуто дробного порядка. Единственность поставленной задачи доказывается методом интегралов энергии, а существование – методом интегральных уравнений.
References
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B. I. Islomov, O. Kh. Abdullayev. Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi–Kober operators of fractional order. Russian Mathematics, 2020, Vol. 64, No. 10, pp. 29–42.
Khubiev K.U. On a boundary value problem for a loaded equation of a mixed hyperbolic-parabolic type. Dokl. Adyg. (Circassian.) Intern. acad. sciences. 2005.
Abdullaev O. Kh. A nonlocal problem for a loaded mixed-type equation with integral operator. Vestnik Sam. state tech. university. Series of Physics and Mathematics. 2016.
Abdullaev O.Kh. Some problems for the degenerate mixed type equation
involving Caputo and Atangano-Baleanu operators fractional order. Progr. Fract. Differ. Appl. 6, No. 2, 1-14 (2020)
Sabitov K. B., Melisheva E. P. The Dirichlet problem for a loaded mixed-typeequation in a
rectangular domain, Russian Math. 2013. 57( 7). pp. 53-65.
Sabitov K.B. An initial-boundary value problem for a parabolic-hyperbolic equation with
loaded terms, Russian Math. 2015.59 (6). pp. 23-33.
Ramazanov M.I. On a nonlocal problem for a loaded hyperbolic-elliptic equation in a rectangular domain. // Mat. magazine. Almaty. 2002.2 (4). pp. 75–81
Salakhitdinov M.S., Karimov E.T. On a nonlocal problem with conjugation conditions of the integral form for the parabolic-hyperbolic one with the Caputo operator. Reports of the Academy of Sciences of the Republic of Uzbekistan. 2014. No. 4. pp.6-9.
Abdullaev O. Kh. Gellerstedt type problem with integral gluing condition for a mixed type
equation with non-linear loaded term. Lobachevskii Journal of Mathematics, 2021, Vol. 42, No. 3, pp. 479–489
Smirnov M.M. Mixed type equations. M .: Higher school. 1985.304 p.
Mikhlin S.G. Lectures on linear integral equations. M .: Fizmatgiz. 1959.232 p.
Miller K.S., Ross B. An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York. 1993.
Podlubny I. Fractional Differential Equations. Academic Press. New York. 1999. 364 p.
Samko S.G., Kilbas A.A., Marichev O.I. Integrals and derivatives of fractional order and some of their applications. Minsk: Science and Technology. 1987.688 p.
Pskhu A.V. Fractional partial differential equations. Moscow: Nauka, 2005.199 p.
Kadirkulov B. J. Boundary problems for mixed parabolic-hyperbolic equations with two lines of changing type and fractional derivative. Electronic Journal of Differential Equations. 2014. 2014(57) . pp. 1–7.
Karimov E.T., Akhatov J.A. Boundary value problem with integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional derivative. Electronic Journal of Differential Equations. 2014. 2014(14). pp. 1–6.
Ashurov R.R., Cabada A., Turmetov B.Kh. Operator method for construction of solutions of linear fractional differential equations with constant coefficients. Fract. Calc. & Appl. Anal.Springer, 2016. 19(1). pp. 229-251.
Islomov B. I., Yuldashev T. K., Ubaydullayev.U.Sh. On Boundary Value Problems for a Mixed
Type Fractional Differential Equation with Caputo Operator. Bulletin of the Karaganda
University. Mathematics series. 2021. 1(101). pp.127-137.
Nakhushev A.M. Equations of Mathematical Biology. M .: Higher school, 1995. 301p.
Nakhushev A.M. Loaded equations and their applications. M .: Science. 2012.233p.
Kaziev V.M. Goursat problem for one loaded integro-differential equations. Differential. equations. 1981. T. 17. No 2. pp. 313–319.
B. I. Islomov1, O. Kh. Abdullayev, N. K. Ochilova. On a problem for the loaded degenerating mixed type equation involving integral-differential operators. Nanosystems: physics, chemistry, mathematics, 2017, 8 (3), p. 1{12}
B. I. Islomov, O. Kh. Abdullayev. Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi–Kober operators of fractional order. Russian Mathematics, 2020, Vol. 64, No. 10, pp. 29–42.
Khubiev K.U. On a boundary value problem for a loaded equation of a mixed hyperbolic-parabolic type. Dokl. Adyg. (Circassian.) Intern. acad. sciences. 2005.
Abdullaev O. Kh. A nonlocal problem for a loaded mixed-type equation with integral operator. Vestnik Sam. state tech. university. Series of Physics and Mathematics. 2016.
Abdullaev O.Kh. Some problems for the degenerate mixed type equation
involving Caputo and Atangano-Baleanu operators fractional order. Progr. Fract. Differ. Appl. 6, No. 2, 1-14 (2020)
Sabitov K. B., Melisheva E. P. The Dirichlet problem for a loaded mixed-typeequation in a
rectangular domain, Russian Math. 2013. 57( 7). pp. 53-65.
Sabitov K.B. An initial-boundary value problem for a parabolic-hyperbolic equation with
loaded terms, Russian Math. 2015.59 (6). pp. 23-33.
Ramazanov M.I. On a nonlocal problem for a loaded hyperbolic-elliptic equation in a rectangular domain. // Mat. magazine. Almaty. 2002.2 (4). pp. 75–81
Salakhitdinov M.S., Karimov E.T. On a nonlocal problem with conjugation conditions of the integral form for the parabolic-hyperbolic one with the Caputo operator. Reports of the Academy of Sciences of the Republic of Uzbekistan. 2014. No. 4. pp.6-9.
Abdullaev O. Kh. Gellerstedt type problem with integral gluing condition for a mixed type
equation with non-linear loaded term. Lobachevskii Journal of Mathematics, 2021, Vol. 42, No. 3, pp. 479–489
Smirnov M.M. Mixed type equations. M .: Higher school. 1985.304 p.
Mikhlin S.G. Lectures on linear integral equations. M .: Fizmatgiz. 1959.232 p.
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Published
2023-12-20
How to Cite
У.Х.Дусанова М.С.Даминова М.К.Эсонтурдиева. (2023). НЕЛОКАЛЬНАЯ ЗАДАЧА С ИНТЕГРАЛЬНЫМ УСЛОВИЕМ СКЛЕЙКИ ДЛЯ НАГРУЖЕННОГО УРАВНЕНИЯ СМЕШАННОГО ТИПА С ДРОБНОЙ ПРОИЗВОДНОЙ КАПУТО. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 4(12), 94–101. Retrieved from https://cajmtcs.casjournal.org/index.php/CAJMTCS/article/view/581
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